Abstract
It is the purpose of this paper to discuss some questions on best constants in connection with Jackson-type inequalities for the compound midpoint and trapezoidal rule. To this end representations of the remainders are employed which explicitly exhibit differences of that order which is characteristic for the exactness of the rule. The matter is considered for continuous and R.iemann integrable functions, using ordinary moduli of continuity and τ-moduli, respectively.
Supported by Deutsche Forschungsgemeinschaft Grant No. Ne 171/11-1
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© 1992 Springer Basel AG
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Büttgenbach, B., Lüttgens, G., Nessel, R.J. (1992). On some problems concerning best constants for the midpoint and trapezoidal rule. In: Walter, W. (eds) General Inequalities 6. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 103. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7565-3_31
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DOI: https://doi.org/10.1007/978-3-0348-7565-3_31
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